1. Field of the Invention
The present invention relates to a system and method for extracting a curvature adapted mesh from a three dimensional implicit function data, and more particularly, to a method for generating a curvature adapted isosurface based on Delaunay triangulation, which extracts an initial mesh from an initial three dimensional implicit function data, calculates the directional curvature of a curved surface from the extracted mesh, calculates a set of Delaunay vertexes using the calculated directional curvature for Delaunay space-division, and calculates data for Delaunay triangulation and three dimensional implicit function from the calculated set of the vertexes again.
2. Description of the Related Art
In general, a conventional method of extracting an isosurface by uniformly dividing a space was widely used as a method for visualizing three-dimensional implicit function data or volume data. However, the conventional method of extracting an isosurface had an inefficiency problem. That is, some of areas could not be finely expressed because the uniform resolution was used, and many triangles were used unnecessarily even in a non-detailed area. Particularly, the loss of the detailed parts of a curved space may cause serious problems in a medical imaging, physics simulation, and high quality rendering, which require super high precision. In order to overcome such problems, there have been many studies for developing a method for extracting an isosurface by non-uniformly dividing a space.
Accordingly, a method for obtaining an isosurface by finely dividing a space in a form of an octree was introduced in an article by M. Ohlberger and M. Rumpf, entitled “Hierarchical and adaptive visualization on nested grids” in Computing, 59(4) 269-285, 1997, and another article by Shekhar, Fayyad, Yagel and Cornhill, entitled “Octree based decimation marching cubes surfaces” in Visualizaition'96 335-342. Although the octree based isosurface obtaining method has an advantage of controlling a resolution, it fails to overcome the problems of too many triangles, the cracks between cells having different resolutions, and the connection of T shaped triangles having vertexes at edges thereof. The problems of the octree based isosurface obtaining method were introduced in an article by Bey, entitled “Tetrahedral grid refinement” in Computing, 55(4) 355-378.
Such problems may be solved by dividing a space in a shape of a tetrahedron rather the shape of the octree. If the space is divided in the shape of the tetrahedron, the crack problem does not arise, and the resolutions can be freely controlled while changing the size and the shape of the tetrahedron.
Therefore, there is a demand for developing a method and system for dividing a space in a shape of a tetrahedron and generating a curvature adapted isosurface using the same.